Put the butter in the pan you want to use. On low to medium heat, let it simmer while stirring for 2-3 minutes. It'll start to foam, and after that small brown particles will appear. Be careful not to burn the butter, but do wait until it's a nice shade of brown. This will give your butter a chocolatey, caramel-like taste.
As soon as the butter looks done, take it off the heat and dump your garlic and onions in there. Let them simmer while you chop carrots.
As you chop, put a good handful of carrots into the pan. Put the pan back on the stove. Stir. Add more carrots. Stir. You don't want the butter to burn, but it adds the taste if you roast the carrots with the onions for a bit.
Add some broth. Stir. Add more carrots. There are a ton of carrots in this recipe.
Dump in the rest of the carrots. Put in the rest of your broth. Add a bit of white pepper, and salt if your stock/ broth isn't the salty kind. Cook until the carrots are cooked.
Puree with an immersion blender. Try to get it as smooth as possible - it's worth the trouble.
Serve with a dollop of sour cream or with crispy bacon on top.